diff --git a/luamml-kernel.lua b/luamml-kernel.lua
deleted file mode 100644
index 678fce1..0000000
--- a/luamml-kernel.lua
+++ /dev/null
@@ -1,33 +0,0 @@
-local properties = node.get_properties_table()
-local if_vertical = token.create'ifv@'
-local if_horizontal = token.create'ifh@'
-local iftrue_index = token.create'iftrue'.index
-
-local funcid = luatexbase.new_luafunction'__luamml_kernel_finalize_phantom:'
-token.set_lua('__luamml_kernel_finalize_phantom:', funcid, 'protected')
-lua.get_functions_table()[funcid] = function()
-  -- TODO: Error handling etc
-  -- At this point, box 0 contains the inner expression and the curent list ends with the noad whose nucleus should get replaced
-  local boxnum = 0
-  local startmath = tex.box[boxnum].list
-  assert(startmath.id == node.id"math")
-  local nucl = assert(tex.nest.top.tail.nucleus)
-  local props = properties[nucl]
-  if not props then -- very likely
-    props = {}
-    properties[nucl] = props
-  end
-  assert(not props.mathml_table)
-  local saved_props = assert(properties[startmath])
-  local saved_core = saved_props.saved_mathml_core
-  local saved = assert(saved_props.saved_mathml_table or saved_core)
-  -- The following could be optimized for the case that both if_vertical and if_horizontal
-  -- are set, but that should't happen ayway and is just supported for consistency.
-  if if_vertical.index ~= iftrue_index then
-    saved = {[0] = 'mpadded', height = 0, depth = 0, saved}
-  end
-  if if_horizontal.index ~= iftrue_index then
-    saved = {[0] = 'mpadded', width = 0, saved}
-  end
-  props.mathml_table, props.mathml_core = saved, saved_core
-end
diff --git a/luamml-patches-kernel.sty b/luamml-patches-kernel.sty
index 1ae497a..e150a33 100644
--- a/luamml-patches-kernel.sty
+++ b/luamml-patches-kernel.sty
@@ -1,17 +1,35 @@
 \ProvidesExplPackage {luamml-patches-kernel} {2021-05-30} {0.0.1-alpha}
   {Feel free to add a description here}
 
-\lua_now:n { require'luamml-kernel' }
-
-\cs_set:Npn \mathph@nt #1 #2 {
+\cs_new:Npn \__luamml_kernel_phantom:nnn #1#2#3 {
   \hbox_set:Nn \c_zero_int {
     $
     \m@th
-    #1
-    {#2}
-    \luamml_flag_save:nNn {} #1 {mphantom}
+    #2
+    {#3}
+    \luamml_flag_save:nNn {mathphant_#1} #2 {mphantom}
+    \luamml_pdf_write:
     $
   }
-  \finph@nt
-  \__luamml_kernel_finalize_phantom:
+  \luamml_annotate:nen {1} {
+    nucleus = true,
+    core = {[0] = 'mpadded',
+      \ifh@\else
+        width = 0,
+      \fi
+      \ifv@\else
+        height = 0, depth = 0,
+      \fi
+      data.mathml.mathphant_#1,
+    }
+  } {
+    \finph@nt
+  }
+}
+\cs_generate_variant:Nn \__luamml_kernel_phantom:nnn {V}
+
+\int_new:N \g__luamml_kernel_phantom_int
+\cs_set:Npn \mathph@nt {
+  \int_gincr:N \g__luamml_kernel_phantom_int
+  \__luamml_kernel_phantom:Vnn \g__luamml_kernel_phantom_int
 }
diff --git a/luamml.dtx b/luamml.dtx
index 9606158..e577199 100644
--- a/luamml.dtx
+++ b/luamml.dtx
@@ -439,10 +439,11 @@
 %    \end{macrocode}
 % \end{macro}
 %
-%
+% We currently provide minimal patching for the kernel, \pkg{amsmath} and \pkg{array}.
+% Currently only the kernel code supports pdf\TeX, but it's planned to extend this.
 %    \begin{macrocode}
-%<*luatex>
 \RequirePackage { luamml-patches-kernel }
+%<*luatex>
 \__luamml_patch_package:n {amsmath}
 \__luamml_patch_package:n {array}
 %</luatex>